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Starting from a nondecreasing function , we introduce a M\"obius-invariant Banach space of functions analytic in the unit disk in the plane. We develop a general theory of these spaces, which yields new results and also, for special choices of , gives most basic properties of -spaces. We have found a general criterion on the kernels and , , such that , as well as necessary and sufficient conditions on so that or , where the Bloch space and the Dirichlet space are the largest, respectively smallest, spaces of -type. We also consider the meromorphic counterpart of and discuss the differences between -spaces and -classes.